Put our bracelet on and don't let those numbers trouble you any more!
Is this correct? I am not sure about using the phrasal verb put on together, or separated by a noun :)
And in the second part of sentence, is those used correctly?
English Language Learners Stack Exchange is a question and answer site for speakers of other languages learning English. It only takes a minute to sign up.Sign up to join this community
I won't touch the numbers part because the reasons or better call them issues you mention in your comments are not the numbers though most of them are expressed with some numeric values.
Okay, the first part: If you want to put on with put, go for it, that's okay!
on in put on serves as an adverbial particle. And, they can go between the verb and the object noun. Said that, **Put on our bracelets* is utterly grammatical. I can recall one of the examples from Swan's PEU on this where
Switch off the light (or similar kind of sentence) was said correct [However, This does not mean that they are always together. Read some more examples where these particles are detached from the verb and placed after the object.
Now the second part.
The pronoun those is okay if you have already mentioned what those numbers are. In other words, if this is the first sentence of any literature, those does not make any sense. You need to mention first what those is as a general rule of pronouns that replace nouns.
Answering questions in order:
In English, Demonstratives denote their proximity (closeness) to the speaker. The words this and these denote they are close (proximal), while the words that and those denote that they are further away (distal). To illustrate, these cups in my hands are much closer than those cups on the far end of the table.
Tying that back to the example sentence, the word those denotes that the numbers are a distance away from the speaker. Therefore, if the numbers are displayed on a screen across the room, or written on a piece of paper in the next room, the usage would be correct. Even if the numbers in question are a group of rabid living numerals which have been caught and dragged into cages in a different building, the use of those would be correct.
If, however, the numbers are displayed on a nearby monitor, or written on the very bracelet being put on which is in the hands of the speaker, the correct word to use would be these.